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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration
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A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. If the total height of the toy is 15.5 cm, find the total surface area of the toy.
Solution:
The given toy is the combination of cone and hemisphere so we need to add the curved surface area of both to get the total surface area of the toy.
Given radius of the cone, r = 3.5 cm
Radius of hemisphere, r = 3.5 cm
Total height of the toy = 15.5 cm
Height of the cone = 15.5 – 3.5 = 12 cm
Slant height of the cone, l = √(h2+r2)
l = √(122+3.52)
l = √(144+12.25)
l = √(156.25)
l = 12.5 cm
Total surface area of the toy = curved surface area of cone + curved surface area of the hemisphere
= π rl + 2π r2
= π r(_l+_2r)
= (22/7)×3.5×(12.5+2×3.5)
= (77/7)×(12.5+7)
= 11×19.5
= 214.5 cm2
Hence the total surface area of the toy is 214.5 cm2.
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